$$\sin x
ps:
By differentiation, monotonicity and Taylor formula, all are wrong, because (sinx)′=cosx must use lim, and this formula must use \sin x< x. This is vicious circle.
If we use Taylor series of \sin x to define \sin x, strictly prove $\sin x
Answer
We can define \sin x as power series. Applying the knowledge of power series, obtain the derivative of \sin x, and then we will easy prove the inequality. Concluding geometry of \sin x, please refer to this.
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